Public, medical, commercial, robotic and military applications can be enhanced with static or mobile wireless sensor nodes (sensors for sensing an environment and transceivers for communicating sensed data). In many such applications, accurate positioning of the nodes is an important task. As used herein, the term positioning means to determine the coordinates or locations of the nodes.
Accurate positioning needs to deal with varying propagation delays in wireless channels, as well as software and hardware design limitations. A Global positioning system (GPS) can provide acceptable accuracies outdoors. Indoors, the accuracies of the GPS is severely degraded by multipath propagation, and a probability of non-line of sight (NLOS) conditions because the GPS needs to have LOS to at least four GPS satellites.
Distributed positioning methods iteratively determine a ranging estimate by sharing range and position information among nodes using either direct ranging (DR) or extended ranging (ER). The distinction is based on the method used to estimate distance between anchor nodes (anchors) at known positions, and sensor node (sensors) at unknown positions.
In DR, the sensor only obtains direct range estimates to anchors. When the sensor has range measurements to three or four anchors, it is possible to obtain a two- or three-dimensional position estimate for the sensor. Then, the sensor can be transformed to another anchor.
In ER, the sensors estimate the distances between each other and a set of anchors. The sensors obtain the distance estimate through a variety of methods, including counting the number of hops along the wireless route to the anchors, measuring the distances to the anchors, and adding all distances of the route, or obtain a geometric estimate of the distance by relying on the relative position of adjacent nodes.
DR is more accurate because the range error between nodes is measured directly and thus positioning error propagation is minimized. However, DR requires a minimum anchor node density.
ER is less accurate because the distance to an anchor is not always directly measured. Instead, some distances are estimated by either the number of hops or geometric estimation. Although ER has less stringent density requirements, positioning error propagation is a problem. Location estimations of nodes further away from the anchor nodes generally have more error than the nodes that are in direct communication contact with the anchor nodes.
It is desired to minimize positioning error propagation while performing extended ranging.